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Thread: Make a table...

  1. #1
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    Make a table...

    Make a table showing all the values of the functions u4 : Z15 ->Z15.

    The function u
    a defined by the rule x ->ax is a bijection Zm ->Zm.



    How is this done? Thanks...
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by jzellt View Post
    Make a table showing all the values of the functions u4 : Z15 ->Z15.

    The function u
    a defined by the rule x ->ax is a bijection Zm ->Zm.



    How is this done? Thanks...
     (4,15)=1 \implies \{4\cdot1, 4\cdot2,\cdot\cdot\cdot, 4\cdot 15\} = \{1,2,\cdot\cdot\cdot,15\}

    Therefore  u_4(\mathbb{Z}_{15}) = \mathbb{Z}_{15} .

     \begin{array}{r|r||r|r}a&u_4(a)&a&u_4(a)\\ \hline 0&0&8&2\\1&4&9&6\\2&8&10&10\\3&12&11&14\\4&1&12&3\  \5&5&13&7\\6&9&14&11\\7&13\end{array}
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  3. #3
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    Thanks for the quick reply, but I'm still not seeing what my table should look like...
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by chiph588@ View Post
     \begin{array}{r|r||r|r}a&u_4(a)&a&u_4(a)\\ \hline 0&0&8&2\\1&4&9&6\\2&8&10&10\\3&12&11&14\\4&1&12&3\  \5&5&13&7\\6&9&14&11\\7&13\end{array}
    Here you go.
    Last edited by chiph588@; Mar 26th 2010 at 06:28 PM.
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